Projective plane curves whose automorphism groups are simple and primitive

We study complex projective plane curves with a given group of automorphisms. Let $G$ be simple primitive subgroup $\mathrm{PGL}(3, \mathbf{C})$, which is isomorphic to $\mathfrak{A}_{6}$, $\mathfrak{A}_{5}$ or $\mathrm{PSL}(2, \mathbf{F}_{7})$. obtain necessary and sufficient condition on $d$ for the existence nonsingular curve degree invariant under $G$. also an analogous problem integral curves.